Odds and probability · Introduction to AI

Probability is the language of uncertain things. When Khalti’s fraud system flags a transaction as 73% likely to be fraud, it is saying something careful. Of all the historical transactions that looked very similar to this one, 73 in every 100 turned out to be fraud. That is a claim about a class of transactions, not about your specific one.

Confuse those two — treat the probability as a verdict on this particular transaction — and you make the most common, and most damaging, mistake in deployed AI.

Probability: a number between 0 and 1

A probability is just a number between 0 and 1 that expresses how likely something is.

P = 0 means the event is impossible.
P = 1 means the event is certain.
P = 0.5 means it is as likely to happen as not.

For two mutually exclusive outcomes — fraud or not fraud, rain or no rain — the probabilities sum to 1. If Khalti says P(fraud) = 0.73, it is also saying P(not fraud) = 0.27.

For more than two outcomes, the probabilities of all of them sum to 1. If a weather model says P(sunny) = 0.4, P(cloudy) = 0.4, P(rain) = 0.2, those three add to 1 and cover all the possibilities the model considers.

Odds: the other way to talk about chance

Probability is one way to express likelihood. Odds is another. The two are interchangeable but written differently.

If the probability of an event is p, the odds are p : (1 − p). A probability of 0.75 corresponds to odds of 3:1. A probability of 0.5 corresponds to odds of 1:1 (a fair coin).

Odds are popular in two places: betting, where 3:1 means “win three for every one you stake,” and Bayes’ rule, which we will meet in the next section. Bayes’ rule is much easier to remember in odds form than in probability form. If you only ever read the next section once, you will still benefit from knowing what 3:1 odds means.

Conditional probability

Here is the most important idea in the chapter. The probability of an event can change when new information arrives. The probability of fraud, given that a transaction is at 3am, is different from the probability of fraud given that it is at noon. The probability of rain in Kathmandu, given that it is Asar, is much higher than the probability in Magh.

We write this as P(A | B) and read it “the probability of A, given B.” The bar is doing all the work.

P(fraud) = 0.001 — across all Khalti transactions ever, the fraction that are fraud is small.
P(fraud | transaction at 3am from a new device) = 0.40 — but among transactions at 3am from a device the user has never used, the fraction that are fraud is much higher.

The two numbers are about the same event — fraud — but they answer different questions, because the condition is different. This distinction breaks down constantly in newspaper reporting on AI.

How probability is misread

Three habits show up everywhere in AI coverage. Spotting them is half the job of AI literacy.

Treating a probability as a yes/no. A model says P(fraud) = 0.85. The newspaper headline says “AI says transaction is fraud.” But the model said no such thing. It said that out of similar transactions, 15% are not fraud. Whether to block, challenge, or allow the transaction is a policy choice on top of the probability, not a verdict from the model.

Treating a low probability as zero. A radiology model says P(cancer) = 0.02. A doctor sees “low risk” and moves on. But P = 0.02 across a screening programme of 50,000 patients means about 1,000 of them have cancer. The probability is small for any one patient; in aggregate it is huge.

Treating a high probability as certainty. A model says P(success) = 0.95. The 5% chance of failure is still there. If you deploy the model on a million users, you will see 50,000 failures. A “95% accurate” system is only acceptable when failure is cheap.

These misreadings are not technical. They are about translation between the model’s careful claim and the decision a human has to make. AI literacy lives in that gap.

A worked example: Khalti’s fraud score

A Khalti transaction comes in at 11pm. The model returns P(fraud) = 0.65. What should the system do?

The answer depends on policy.

Block the transaction. Safe, but the user is locked out. 35% of users in this situation are wrongly blocked. Whether that’s acceptable depends on the transaction size — for Rs. 500 it probably isn’t; for Rs. 500,000 it might be.
Send an OTP challenge. A middle path. If the user can answer, allow the transaction. This catches most fraud (which can’t answer the OTP) while inconveniencing legitimate users only briefly.
Allow it. Risky. 65% of these transactions are fraud, and money will be lost.

Notice: the probability is the same in all three cases. The decision is different because the policy is different. The same model, deployed with different policies, produces a system that is good for users in one case and terrible in another. This is why probability is not policy, and AI literacy is also literacy in policy.

Check your understanding

Quick check

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A weather model reports P(rain tomorrow) = 0.3. What is P(no rain tomorrow), assuming rain and no-rain are the only outcomes the model considers?

Quick check

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A radiology screening programme for 50,000 patients uses a model that reports P(cancer) = 0.02 for each patient. What is the most accurate reading of this number?

It is so small we can treat it as zero — no further action needed.
2% of patients in this group are expected to have cancer — about 1,000 patients in absolute terms.
The model is broken.
Every patient has a 2% piece of cancer somewhere.

What comes next

We have the vocabulary. The next section is about the single most important equation in this course: Bayes’ rule. It tells you how to update a probability when new evidence arrives — and it will explain why a 95%-accurate cancer test, applied to a healthy population, mostly produces false positives.